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Math Help - need help with this proof

  1. #1
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    need help with this proof

    Hi ppl, pretty new to maths. picked up a discrete mathematics unit this semester at uni for something a little different. got a quick question.

    Question: given that n is an integer, prove that n is even if and only if 9n2 + 4n - 11 is odd.

    Now, i already know that the above is true. just wondering what is the general accepted format to answer this type of question? i dont know what my answer is supposed to look like so could someone maybe do a quick demonstration proof of this question so i can see how this works?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by dogma View Post
    Hi ppl, pretty new to maths. picked up a discrete mathematics unit this semester at uni for something a little different. got a quick question.

    Question: given that n is an integer, prove that n is even if and only if 9n2 + 4n - 11 is odd.

    Now, i already know that the above is true. just wondering what is the general accepted format to answer this type of question? i dont know what my answer is supposed to look like so could someone maybe do a quick demonstration proof of this question so i can see how this works?
    9n^2+4n-11\equiv n^2-1\text{ mod }2

    Clearly then n\text{ even}\Leftrightarrow n\equiv0\text{ mod }2\Leftrightarrow n^2-1\equiv1\text{ mod }2\Leftrightarrow 9n^2+4n-11\text{ odd}
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  3. #3
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    cheers
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